Generic Bayer Species Model
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Related Links: Alumina3, Alumina 1 vs Alumina 3, Converting Alumina 1 to Alumina3
General Description
IMPORTANT NOTE: Alumina1 models are not distributed and supported with SysCAD 9.3. SysCAD 9.3 version of Alumina1 is available on request for project conversion purposes.
NOTE: Recommended alternate Bayer Species Model is Alumina 3 Bayer Species Model
The Generic Bayer species model is used to calculate the properties of fluids within an Alumina project using equations defined in the public domain. These equations are documented in the Model Theory section given below.
General information regarding the Bayer species models, such as heats of reaction, volume displays, etc. is given in General Bayer Data.
All of the properties that are not explicitly calculated by this model are calculated using the Standard Species Model.
Model Theory
The calculations for liquor and slurry densities, heat capacity and boiling point elevation are evaluated using the following formulae:
The variables used in the calculations are described below:
A | = | Al_{2}O_{3} concentration (g/L liquor) at the slurry temperature |
C | = | NaOH concentration, expressed as grams Na_{2}CO_{3}/L liquor @ the slurry temperature |
A_{25} | = | Al_{2}O_{3} concentration (g/L liquor) at 25°C. |
C_{25} | = | NaOH concentration, expressed as grams Na_{2}CO_{3}/L liquor @ 25°C. |
T | = | Temperature in °C |
T_{k} | = | Temperature in K |
T_{Na} | = | The sum of all sodium salts, caustic, carbonate, organics, NaCl, Na2SO4, all expressed as Na2CO3 @ 25°C. The engineering units for this is Concentration (mass/mass) wt%. |
- [math]\displaystyle{ \mathbf{\mathit{T_{Na}=\left([Na_2CO_3]+\left(\frac{[NaOH]}{2*MW(NaOH)}+\frac{[Na_2C_2O_4]}{MW(Na_2C_2O_4)}+\frac{[Na_{org}]}{MW(Na_2C_5O_7)}+\frac{[NaCl]}{2*MW(NaCl)}+\frac{[Na_2SO_4]}{MW(Na_2SO_4)}\right)*MW(Na_2CO_3)\right)*\frac{100}{L_m}}} }[/math]
- where: L_{m} - Liquor mass flow (engineering units need to be the same as individual salts in the equation.)
T_{Al2O3} = Total concentration (mass/mass) wt% of Alumina.
- [math]\displaystyle{ \mathbf{\mathit{T_{Al203}=Al_20_3*\frac{100}{L_m}}} }[/math]
- where L_{m} - Liquor mass flow, engineering units used should be the same as for Al2O3 in the equation.
TOC_{25} = Total Organic carbon (Na_{2}C_{5}O_{7} + Na_{2}C_{2}O_{4}) expressed as g/L Carbon @ 25°C;
Density Calculations
Liquid SG @ T^{1}
- [math]\displaystyle{ \mathbf{\mathit{LSG_T=LSG_{25}*\left\lfloor1-\left(0.0005021858*0.85\left(T-25\right)\right)-\left(0.0000011881*0.85\left(T-25 \right)^2\right)\right\rfloor}} }[/math]
- where: LSG_{25} -- liquid SG @ 25°C
Liquid SG @ 25°C^{1}
- [math]\displaystyle{ \mathbf{\mathit{LSG_{25}=\begin{matrix}&0.982+\left(0.01349855*T_{Na}\right)+\left(-0.00024948*T^2_{Na}\right)+\left(0.00000273*T^3_{Na}\right)\\ &+\left(0.00208035*T_{Al203}\right)+\left(0.00004113*T^2_{Al203}\right)+\left(-0.00000728*T^3_{Al203}\right)+\left(0.00033367*T_{Na}*T_{Al203}\right)\end{matrix}}} }[/math]
- where:
- T_{Na} Total concentration (mass/mass) wt% of Sodium, reported as Na_{2}CO_{3}.
- T_{Al2O3} Total concentration (mass/mass) wt% of Alumina.
- where:
Slurry SG @ T
- [math]\displaystyle{ \mathbf{\mathit{S_LSG=\frac{SolidsMass+LiquidsMass}{SlurryFlow}}} }[/math]
- [math]\displaystyle{ \mathbf{\mathit{SlurryFlow=\frac{SolidsMass}{SolidsSG}+\frac{LiquidsMass}{LSG_T}}} }[/math]
Slurry SG @ 25°C
- [math]\displaystyle{ \mathbf{\mathit{S_LSG_{25}=\frac{SolidsMass+LiquidsMass}{SlurryFlow\ 25^{\circ} C}}} }[/math]
- [math]\displaystyle{ \mathbf{\mathit{SlurryFlow=\frac{SolidsMass}{SolidsSG}+\frac{LiquidsMass}{LSG_{25}}}} }[/math]
Heat Capacity Calculations
Liquid Heat Capacity^{1}
- [math]\displaystyle{ \mathbf{\mathit{Cp_L=\begin{pmatrix}1.0275057375729-0.020113606661083*T_{Na2O}\\ +0.001081165172606*T^2_{Na2O}-0.000022606160779*T^3_{Na2O}\\ -0.004597725999883*T_{Al2O3}-0.000001053264708*T^2_{Al2O3}-0.00000218836287*T^3_{Al2O3}\end{pmatrix}*4.184}} }[/math]
- where [math]\displaystyle{ \mathbf{\mathit{T_{Na2O}=T_{Na}*\frac{MW(Na_2O)}{MW(Na_2CO_3)}}} }[/math]
This is scaled for dilute liquors where [math]\displaystyle{ \mathit{T_{Na2O}} }[/math] as liquid weight % is less than 0.19.
Solids Heat Capacity
Solids Cp (Cp_{s}) is calculated from Cp values as given in the species database (ie using Standard Species Model).
Slurry Heat Capacity
- [math]\displaystyle{ \mathbf{\mathit{Cp_{sL}=\frac{SolidsMass*Cp_s+LiquidsMass*Cp_L}{SolidsMass+LiquidsMass}}} }[/math]
Boiling Point Elevation^{2}
The Boiling Point Elevation method is selected globally from the Feeder unit operation as illustrated below. NOTE: The feeder must be using the Bayer species model.
Method 1: Dewey Equation
- [math]\displaystyle{ \mathbf{\mathit{BPE=\begin{matrix}&0.00182+0.55379*\left(\frac{M}{10}\right)^7+0.004060625*M*T_L\\ &+\frac{1}{T_K}*\left(-286.66*M+29.919*M^2+0.6228*M^3\right)-0.032647*M*\left(M*\frac{T_K}{1000}\right)^2\\ &+\left(\frac{T_K}{1000}\right)^5*\left[5.9705*M-\left(0.57532*M^2\right)+\left(0.10417*M^3\right)\right] \end{matrix}}} }[/math]
Where M is the Total Molality of the solution, calculated using the following species: Al_{2}O_{3}, NaOH, Na_{2}CO_{3}, NaCl, Na_{2}SO_{4}, Na_{2}C_{5}O_{7} and Na_{2}C_{2}O_{4}. T_{k} is the Saturated temperature for pure water at the stream Pressure.
Method 2: Adamson Equation
- [math]\displaystyle{ \mathbf{\mathit{BPE=\begin{matrix}&0.007642857+0.006184282*X+2.92857e^{-5}*T+0.00010957*X^2-3.80952e^{-8}*T^2\\ &+0.000208801.XT-8.61985e^{-10}*X^3-8.61985e^{-10}*T^3+1.7316e^{-10}*XT^2-2.49763e^{-7}*X^2T\end{matrix}}} }[/math]
- Where:-- X = Total Soda concentration expressed as g/L Na2O @ 25C; and
- T = temperature in degree C.
NOTE: Constants in the above equation were determined by data fitting of published Adamson data.
Saturated Alumina Concentration^{3}
- [math]\displaystyle{ \mathbf{\mathit{A^{*} = \cfrac{0.96197 C_{25}} {1+\cfrac{ 10 ^{\left(\cfrac{\alpha_o \sqrt{I}} {1+ \sqrt{I}} \right)- \alpha_3 I - \alpha_4 I^{\frac{3}{2}} }} {{exp \left({\cfrac{\Delta G_{rxn}}{RT}}\right)}}}}} }[/math]
- Where a, a_{3}, and a_{4} are constants (see table 1)
- DG_{RXN} is the Gibbs energy of dissolution (-30960 J/mol)
- I is the ionic strength, calculated using the following equation:
- [math]\displaystyle{ \mathbf{\mathit{I=0.01887C_{25}+\frac{k_1\left[NaCl\right]}{MW(NaCl)}+\frac{k_2\left[Na_2CO_3\right]}{MW(Na_2CO_3)}+\frac{k_3\left[Na_2SO_4 \right]}{MW(Na_2SO_4)}+k_40.01887*TOC_{25}}} }[/math]
- Where k_{1},k_{2}, k_{3} and k_{4} are constants (see Table 1)
- Concentration of salts and carbonate are @ 25 °C.
Table 1
a_{} | a_{3} | a_{4} | k_{1} | k_{2} | k_{3} | k_{4} |
---|---|---|---|---|---|---|
-9.2082 | -0.8743 | 0.2149 | 0.9346 | 2.0526 | 2.1714 | 1.6734 |
Oxalate Equilibrium
Calculates the equilibrium concentration (g/l) of oxalate, based on stream properties.
(Equation from British Aluminium - Burnt Island)
- [math]\displaystyle{ \mathbf{\mathit{OxEquil=7.62*Exp\left[0.012T-\left(\frac{MW(Na_2O)}{MW(Na_2CO_3)}\right)*\left(0.016*C_{25}+\frac{0.011*Qm_{Na_2CO_3}} {Qv}\right)\right]}} }[/math]
- Where Qv = Liquor Volume at 25 °C.
- Qm_{Na2CO3 }= Mass flowrate of sodium carbonate
- T = temperature in °C.
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Stream Property Limits
One limitation the Generic Bayer Species model (Alumina1) has is that under some (normally unrealistic) circumstances, the density equation can return very unrealistic values. This is because the Bayer species model uses dissolved alumina in terms of separate Al_{2}O_{3}(aq) and NaOH(aq) species, instead of the naturally occurring NaAl[OH]_{4} species (which is used Alumina3). In this form, it is possible for the user to mistakenly input stream composition containing Al_{2}O_{3}(aq) with no NaOH(aq). In this case, the A/C will be infinite and the density equation will return very incorrect value of 0 kg/m^{3}.
To safe guard this situation, the Bayer stream property has been bound to the following limits:
- The minimum density that can be returned is 700 kg/m^{3}
- The maximum A/C that would be returned is 0.96 - this is the A/C value of NaAl[OH]_{4} with no free caustic present.
- The maximum RP (A/C_{Na2O}) that would be returned is 1.641 - this is the A/C value of NaAl[OH]_{4} with no free caustic present.
References:
- Molloy-Donaldson Model
- Dewey, J.K.L. Boiling Point Rise of Bayer Liquors. Light Metals 1981. The Metallurgical Society of AIME pp 185 -- 197.
- Rosenberg S.P and Healy S.J. A Thermodynamic Model for Gibbsite Solubility in Bayer Liquors. Fourth International Alumina Quality Workshop. June 1996.
Data Sections
The data will be displayed on the Qi and Qo pages of the Pipe access window, and under the Content page for units. Only the data that is calculated using the Bayer equations is shown below. The other data is discussed in the SysCAD Model help - Pipe Section.
Feeder Configuration Data
Tag / Symbol | Input / Calc | Description |
Global Bayer Constants and Options: | ||
BPE_Method | Dewey | This is the original method implemented in SysCAD. This method becomes inaccurate in high caustic concentration range. |
Adamson | This method is more accurate in the high caustic concentration range. See Boiling Point Elevation for equations used. | |
BPE_Factor | Input | This field can be used as a "fudge factor" for the Boiling Point Elevation number, if the calculated value using the generic formula differs from actual expected value. Note: this will only adjust the value linearly. |
Rho_Factor | Input | This field can be used as a "fudge factor" for the Bayer Liquor Density number, if the calculated value using the generic formula differs from actual expected value. Note: this will only adjust the value linearly. |
H2OTestFrac0 | Input | This is used handle very dilute concentrations in the stream. If the Water Fraction in the stream is higher than this value, then the stream property will be calculated using the Standard Species Model. The maximum value for this is 99.99%. |
Bayer Liquor Design Values | ||
DefineLiquor | Check Box | If this box is checked, the Feeder will automatically calculate the make-up of the feed stream, based on the variables supplied below. |
DefnLiqMethod | TotOrganics and Ratio | Defines Organics using the Rqd_Organic and Rqd_OrgRatio fields. |
TOC and Oxalate | Defines Organics using the Rqd_TOC and Rqd_Oxalate fields. | |
Rqd_A/C | Input | The required ratio of A:C in the Feed stream, where A is the Al_{2}O_{3} concentration (g/L liquor) and C is the NaOH concentration, expressed as grams Na_{2}CO_{3}/L liquor @ 25^{--}C |
Rqd_C/S | Input | The required ratio of C:S in the Feed stream, where C is the NaOH concentration, expressed as grams Na_{2}CO_{3}/L liquor @ 25^{--}C and S is the NaOH plus Na_{2}CO_{3} concentration, expressed as grams Na_{2}CO_{3}/L liquor @ 25^{--}C. |
Rqd_C | Input | The required value of C in the Feed stream, where C is the NaOH concentration, expressed as grams Na_{2}CO_{3}/L liquor @ 25^{--}C. |
Rqd_SiO_{2} | Input | Required concentration of SiO_{2} in g/L @ 25^{--}C |
Rqd_TOC | Input(Based on DefLiqMethod selected) | Required Total organic carbon concentration in the stream expressed as g/L carbon @ 25 °C. |
Rqd_Oxalate | Required oxalate concentration in the stream expressed as g/L of Na_{2}CO_{3 }@ 25^{--}C | |
Rqd_Organic | Input (Based on DefLiqMethod selected) | Required organic [Na_{2}C_{5}O_{7}(l) + Na_{2}C_{2}O_{4}(l)] concentration in the stream expressed as grams of Na_{2}CO_{3}/L liquor @ 25^{--}C. |
Rqd_OrgRatio | Required ratio of Sodium Oxalate : Total organic in the stream. Where total organic is Rqd_Organic defined above. All concentrations are expressed as grams of Na_{2}CO_{3}/L liquor @ 25^{--}C. | |
Rqd_Na_{2}SO_{4} | Input | Required concentration of Na_{2}SO_{4} in g/L @ 25^{--}C |
Rqd_NaCl | Input | Required concentration of NaCl in g/L @ 25^{--}C |
SolidsFrac | Input | The fraction of solids in the feed. The proportion of the different solid species is maintained. If there are no solid species specified then THA is assumed. |
The following points are essential to the user--s understanding of this feature:
Liquid Specification
The first eight of the above variables are used to define the percentages of the liquid species.
Note: The only liquid species that will be used in calculating the liquid make-up are:
H2O(l) - Water
Al2O3(l) - Alumina
NaOH - Caustic Soda
Na2CO3(l) - Sodium Carbonate
Na2SO4(l) - Sodium Sulphate
NaCl(l) - Sodium Chloride
SiO2(l) - Quartz
Organics:
Na2C2O4(l) - Sodium Oxalate
Na2C5O7(l) - Organic
Solid Specification
The last variable is used to specify the required solids fraction. In addition to this variable, the user must also specify the individual fractions of the solids required on the MF (Mass Fraction) page, as percentages of the SOLIDS flow, NOT as percentages of the entire flow.
Bayer Data
Tag | Symbol | Input or Calc | Description |
SatT@P | Calc | The saturated temperature at the stream pressure |
SatP@T | Calc | The saturated pressure at the stream temperature |
BPE | Calc | The boiling point elevation at the stream composition and temperature. |
Bayer Liquor Values @ 25°C | ||
A | AluminaConc | Calc | Al_{2}O_{3} concentration @ 25°C. (g/L liquor) |
C | CausticConc | Calc | NaOH concentration, expressed as grams Na_{2}CO_{3}/L liquor @ 25°C. |
S | SodaConc | Calc | NaOH plus Na_{2}CO_{3} concentration, expressed as grams Na_{2}CO_{3}/L liquor @ 25°C. |
A/C | Calc | Ratio of A to C, see Stream Property Limits |
C/S | Calc | Ratio of C to S |
Cl/C | Calc | Ratio of Cl to C |
TOC | Calc | Total organic carbon concentration, as carbon equivalent. Grams of [Na_{2}C_{5}O_{7}(l)*5 + Na_{2}C_{2}O_{4}(l)*2] / L liquor @ 25°C. |
SodiumCarbConc | Calc | Sodium Carbonate concentration |
FC | FreeCaustic | Calc | Caustic Concentration excluding the amount assciated with A (Sodium Aluminate NaAl[OH]4), expressed as g/L of Na_{2}CO_{3}. |
SolidsConc25 | Calc | Expressed as grams of solids / L Slurry @ 25°C. |
Concentration @ 25°C, as Na_{2}CO_{3} equivalent | ||
Organates | Calc | Grams of organic Na_{2}C_{5}O_{7}(l) / L liquor @ 25°C. |
Oxalate | Calc | Grams of oxalate Na_{2}C_{2}O_{4}(l) / L liquor @ 25°C. |
TotalOrg | Calc | Grams of [Na_{2}C_{5}O_{7}(l) + Na_{2}C_{2}O_{4}(l)] / L liquor @ 25°C. |
TOOC | Calc | Total organic carbon concentration as Na_{2}CO_{3} equivalent. Grams of [Na_{2}C_{5}O_{7}(l)*5 + Na_{2}C_{2}O_{4}(l)*2] / L liquor @ 25°C |
NaCl | Calc | Grams of NaCl(l) / L liquor @ 25°C. |
Na2SO4 | Calc | Grams of Na_{2}SO_{4}(l) / L liquor @ 25°C. |
TotalNa | Calc | As per T_{Na} Equation in Model Theory section, but expressed as g/L liquor @ 25°C. |
Other properties @ 25°C | ||
LVolFlow25 | Calc | Liquor Volumetric Flowrate @25°C. |
SLVolFlow25 | Calc | Slurry Volumetric Flowrate @25°C. |
LRho25 | Calc | The liquor density @ 25°C. see Stream Property Limits |
SLRho25 | Calc | The slurry density @ 25°C. |
Oxalate* | Calc | Grams of oxalate Na_{2}C_{2}O_{4}(l) / L liquor @ 25°C. |
NaCl* | Calc | Grams of NaCl(l) / L liquor @ 25°C. |
Na2SO4* | Calc | Grams of Na_{2}SO_{4}(l) / L liquor @ 25°C. |
Bayer Liquor Values @ 25 °C, as Na2O Equivalent | ||
C_Na2O | Calc | NaOH concentration, expressed as grams Na_{2}O/L liquor @ 25°C. |
S_Na2O | Calc | NaOH plus Na_{2}CO_{3} concentration, expressed as grams Na_{2}O/L liquor @ 25°C. |
TotalNa_Na2O | Calc | Total Sodium, expressed as grams Na_{2}O/L Liquor @ 25°C. |
RP | Calc | Ratio of A : C expressed as Na_{2}O. see Stream Property Limits |
Bayer Liquor Values @ Temperature | ||
A@T | AluminaConcT | Calc | Al_{2}O_{3} concentration @ Temperature (g/L liquor) |
C@T | CausticConcT | Calc | NaOH concentration, expressed as grams Na_{2}CO_{3}/L liquor @ Temperature. |
S@T | SodaConcT | Calc | NaOH plus Na_{2}CO_{3} concentration, expressed as grams Na_{2}CO_{3}/L Liquor @ Temperature. |
TOC@T | Calc | Total organic carbon concentration as Carbon equivalent. Grams of [Na_{2}C_{5}O_{7}(l)*5 + Na_{2}C_{2}O_{4}(l)*2] / L liquor @ Temperature. |
SolidsConcT | Calc | Expressed as grams of solids / L Slurry @ Temperature. |
BoilPtElev | Calc | The boiling point elevation. |
Bayer Liquor Precipitation Values @ Temperature* | ||
ASat | A_Saturation | Calc | The saturated Alumina concentration @ Temperature. |
A/CSat | Calc | The ratio of ASat : C @ Temperature. |
SSN_Ratio | Calc | The ratio of A : ASat @ Temperature. |
I | IonicStrength | Calc | The Ionic strength. See model theory under Alumina saturation for equation. |
OxalateEq | Calc | The Oxalate Equilibrium value. See Model Theory for equation. |
Alumina Particle Size Info (Under Tab SSA or MF if component list is short) Please see Specific Surface Area (SSA) | ||
Method | Display | |
SetData | Tickbox | Allows the user to set values for SAM |
Solids | List | Allows the user to select the solid component to base the calculation on. Note: The selected compound's flowrate must be none zero for the propagation of the following parameters to downstream unit operations. |
SAM | SeedSurfaceAreaM | Input | Seed Surface Area, Mass basis (m^2/g) |
SAL | SeedSurfaceAreaL | Calc | Seed Surface Area, Volume basis (m^2/L) |
#/s | Calc | Particle number per second |
#/L | Calc | Particle number per litre. |
D | PartDiam | Input | Particle diameter in μm. |
SolidsQm | Calc | The amount of solids (eg: Al2O3.3H2O) present. |
Please refer to Hints and Comments of the Precipitation Model for more info.